Scala analysis: 12_fun
Rational well temperament based on 577/289, 3/2, and 19/16.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/18 93.603014 undevicesimal semitone 2: 18464/16473 197.534174 3: 19/16 297.513016 19th harmonic 4: 361/288 391.116031 5: 1154/867 495.047191 6: 361/256 595.026032 two (19th harmonic) 7: 73856/49419 695.579174 8: 10963/6936 792.560207 9: 9232/5491 899.489175 10: 4616/2601 993.092190 11: 208297/110976 1090.073223 12: 577/289 1197.002191
SHOW/INTERVAL
0: 384/361 106.9290 1: 19/18 93.6030 undevicesimal semitone 2: 110784/104329 103.9312 3: 312987/295424 99.9788 4: 19/18 93.6030 undevicesimal semitone 5: 110784/104329 103.9312 6: 312987/295424 99.9788 7: 18907136/17840259 100.5531 8: 1083/1024 96.9810 9: 384/361 106.9290 10: 19/18 93.6030 undevicesimal semitone 11: 1083/1024 96.9810 12: 384/361 106.9290
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 19/18 93.603 cents undevicesimal semitone 1: 2 1083/1024 96.981 cents 1: 2 312987/295424 99.979 cents 1: 1 18907136/17840259 100.553 cents 1: 2 110784/104329 103.931 cents 1: 2 384/361 106.929 cents 2: 1 6859/6144 190.584 cents 2: 1 1982251/1772544 193.582 cents 2: 3 18464/16473 197.534 cents 2: 3 64/57 200.532 cents 2: 4 9/8 203.910 cents major whole tone 3: 9 19/16 297.513 cents 19th harmonic 3: 3 2363392/1982251 304.463 cents 4: 2 361/288 391.116 cents 4: 1 20577/16384 394.494 cents 4: 1 5946753/4726784 397.492 cents 4: 2 1181696/938961 398.066 cents 4: 3 6924/5491 401.444 cents 4: 3 24/19 404.442 cents smaller undevicesimal major third 5: 4 1154/867 495.047 cents 5: 4 4/3 498.045 cents perfect fourth 5: 3 171/128 501.423 cents 5: 1 2658816/1982251 508.373 cents 6: 6 361/256 595.026 cents two (19th harmonic) 6: 6 147712/104329 601.976 cents 7: 1 6859/4608 688.629 cents 7: 3 73856/49419 695.579 cents 7: 4 1731/1156 698.957 cents 7: 4 3/2 701.955 cents perfect fifth 8: 3 10963/6936 792.560 cents 8: 3 19/12 795.558 cents undevicesimal minor sixth 8: 2 3249/2048 798.936 cents 8: 1 799.51033 cents 8: 1 9453568/5946753 802.508 cents 8: 2 166176/104329 805.886 cents 9: 3 6859/4096 892.539 cents 9: 9 9232/5491 899.489 cents 10: 4 4616/2601 993.092 cents 10: 3 32889/18496 996.470 cents 10: 3 57/32 999.468 cents undevicesimal minor seventh 10: 1 1022757888/57287053 1003.420 cents 10: 1 3545088/1982251 1006.418 cents 11: 2 208297/110976 1090.073 cents 11: 2 361/192 1093.071 cents 11: 1 61731/32768 1096.449 cents 11: 2 170459648/90453243 1097.023 cents 11: 2 590848/312987 1100.021 cents 11: 3 10386/5491 1103.399 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.36364 = 48/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 93.6 197.5 297.5 391.1 495.0 595.0 695.6 792.6 899.5 993.1 1090.1 1197.0 93.6 : 103.9 203.9 297.5 401.4 501.4 602.0 699.0 805.9 899.5 996.5 1103.4 1197.0 197.5 : 100.0 193.6 297.5 397.5 498.0 595.0 702.0 795.6 892.5 999.5 1093.1 1197.0 297.5 : 93.6 197.5 297.5 398.1 495.0 602.0 695.6 792.6 899.5 993.1 1097.0 1197.0 391.1 : 103.9 203.9 304.5 401.4 508.4 602.0 699.0 805.9 899.5 1003.4 1103.4 1197.0 495.0 : 100.0 200.5 297.5 404.4 498.0 595.0 702.0 795.6 899.5 999.5 1093.1 1197.0 595.0 : 100.6 197.5 304.5 398.1 495.0 602.0 695.6 799.5 899.5 993.1 1097.0 1197.0 695.6 : 97.0 203.9 297.5 394.5 501.4 595.0 699.0 798.9 892.5 996.5 1096.4 1197.0 792.6 : 106.9 200.5 297.5 404.4 498.0 602.0 702.0 795.6 899.5 999.5 1100.0 1197.0 899.5 : 93.6 190.6 297.5 391.1 495.0 595.0 688.6 792.6 892.5 993.1 1090.1 1197.0 993.1 : 97.0 203.9 297.5 401.4 501.4 595.0 699.0 798.9 899.5 996.5 1103.4 1197.0 1090.1: 106.9 200.5 304.5 404.4 498.0 602.0 702.0 802.5 899.5 1006.4 1100.0 1197.0 1197.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.6030 .. 106.9290 cents 6912/6859, 13.3260 cents 19/18, 93.6030 cents 2: 190.5840 .. 203.9100 cents 6912/6859, 13.3260 cents 2476099/2359296, 83.6551 cents 3: 297.5130 .. 304.4631 cents 37814272/37662769, 6.9501 cents 19/18, 93.6030 cents 4: 391.1160 .. 404.4420 cents 6912/6859, 13.3260 cents 715592611/680656896, 86.6529 cents 5: 495.0472 .. 508.3731 cents 6912/6859, 13.3260 cents 10963/10404, 90.6052 cents 6: 595.0260 .. 601.9762 cents 37814272/37662769, 6.9501 cents 715592611/680656896, 86.6529 cents 7: 688.6290 .. 701.9550 cents 6912/6859, 13.3260 cents 715592611/680656896, 86.6529 cents 8: 792.5602 .. 805.8862 cents 6912/6859, 13.3260 cents 10963/10404, 90.6052 cents 9: 892.5390 .. 899.4892 cents 37814272/37662769, 6.9501 cents 715592611/680656896, 86.6529 cents 10: 993.0922 .. 1006.4181 cents 6912/6859, 13.3260 cents 19/18, 93.6030 cents 11: 1090.0732 .. 1103.3992 cents 6912/6859, 13.3260 cents 2476099/2359296, 83.6551 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 19/18, 93.6030 cents, class 1 Average step (divided formal octave): 99.7502 cents Largest one step interval : 384/361, 106.9290 cents Average / Smallest step : 1.065673 Largest / Average step : 1.071968 Largest / Smallest step : 1.142367 Median interval of one step : 312987/295424, 99.9788 cents, amount: 2 Most common interval of one step : 19/18, 93.6030 cents, amount: 3 Least squares average step : 99.35655 cents, oct.: 1192.27862 cents Scale is strictly proper Step pattern alph. order: ABCABCDEFAEF Step pattern size order : AECAECDBFABF Scale is a Constant Structure, by a margin of 83.65508 cents Scale diversity : 1.089964 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.893519 Rothenberg efficiency : 0.393470 redundancy: 0.606530 Efficiency x scale size : 4.721645 Number of different interval sizes : 48 = 4.36364 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 4.36364 = 48/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 0.57430 cents Most common intervals : 19/16, 297.5130 cents & inv., amount: 9 Most common triad is 0.0 297.513 899.489 cents, amount: 6 Number of recognisable fifths : 12, average 698.2513 cents Number of appreciable fifths : 11, average 699.1260 cents Number of recognisable fourths : 12, average 498.7509 cents Best fifths form a closed circle Formal octave complements present : 3 = 25.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions with margin 13.3260 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions with margin 13.3260 cents: 1 2 3 4 5 6 7 8 9 10 11 -- Rational properties -- Prime limit : 577 Odd number limit : too high to compute Highest odd numerator or denominator: 208297 Scale harmonicity : 0.005468 Fundamental : 1/12651264, -23.5928 octaves, 0.0000 Hz. Guide tone : 26662016, 24.6683 octaves, 6975465008.064 Hz. Exponens Consonantiae : 3.373082E+14, 48.26106 octaves Euler's gradus suavitatis : 682 Sum of Mann's harmonic distance : 260774.5, average 21731.20833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 38.79579, average 3.23298 Sum of Tenney's harmonic distance : 77.29653, average 6.44138 Vogel's harmonic complexity : 434.83333 Wille's k value : 8920129 Wilson's harmonic complexity : 674 Rectangular lattice diameter : 8 Triangular lattice diameter : 7 Lattice compactness : 479.96822, average 6.15344 Lattice compactness (without 2's) : 181.18651, average 2.32290 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -8 .. 7 -0.66667 48 3: -2 .. 0 -1.00000 12 17: -2 .. 0 -1.33333 16 19: -1 .. 2 0.50000 12 4 577: 0 .. 1 0.66667 8 8 Average exponent except 2's :-14 / 12 =-1.16667 Average absolute exponent except 2's: 48 / 12 = 4.00000 Scale is weakly epimorphic with val: <12 17 49 51 110| Scale is JI-epimorphic with val: <12 19 49 51 110| = patent Scale is weakly epimorphic with val: <12 20 49 49 110| Scale is weakly epimorphic with val: <12 20 49 51 110| Scale is weakly epimorphic with val: <12 20 49 53 110|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 4.5035 c. M:-7.8847 c. Twelve-tone Chromatic (1/11-comma) 53: 4 5 4 4 5 4 5 4 5 4 4 5 SP M ME SD: 4.5768 c. M: 7.8174 c. 65: 5 6 5 5 6 5 6 5 6 5 5 6 SP M ME SD: 3.3373 c. M: 5.7326 c. 77: 6 7 6 6 7 6 7 6 7 6 6 7 SP M ME SD: 2.6333 c. M:-4.5571 c. 89: 7 8 7 7 8 7 8 7 8 7 7 8 SP M ME SD: 2.2754 c. M:-4.2078 c. 101: 8 9 8 8 9 8 9 8 9 8 8 9 SP M ME SD: 2.1408 c. M:-3.9414 c. 113: 9 10 9 9 10 9 10 9 10 9 9 10 SP M ME SD: 2.1373 c. M:-3.7317 c. 125: 10 11 10 10 11 10 11 10 11 10 10 11 SP M ME SD: 2.2019 c. M:-3.5622 c. 129: 10 11 11 10 11 11 11 10 12 10 10 12 SP D3 SD: 2.1761 c. M: 4.4201 c. 133: 10 12 11 10 12 11 11 11 12 10 11 12 SP D3 SD: 2.0283 c. M: 4.1153 c. 137: 11 12 11 11 12 11 12 11 12 11 11 12 SP M ME SD: 2.2968 c. M:-3.4224 c. 140: 11 12 12 11 12 12 11 12 12 11 11 13 SP T3 SD: 2.2354 c. M: 4.2212 c. 141: 11 12 12 11 12 12 12 11 13 11 11 13 SP D3 SD: 1.7076 c. M: 3.4329 c. 145: 11 13 12 11 13 12 12 12 13 11 12 13 SP D3 SD: 1.5671 c. M: 3.1222 c. 153: 12 13 13 12 13 13 13 12 14 12 12 14 SP D3 SD: 1.3551 c. M: 2.6006 c. 157: 12 14 13 12 14 13 13 13 14 12 13 14 SP D3 SD: 1.2142 c. M: 2.2809 c. 165: 13 14 14 13 14 14 14 13 15 13 13 15 SP D3 SD: 1.1148 c. M: 1.8894 c. 169: 13 15 14 13 15 14 14 14 15 13 14 15 SP D3 SD: 0.9702 c. M: 1.5591 c. 177: 14 15 15 14 15 15 15 14 16 14 14 16 SP D3 SD: 0.9872 c. M: 1.4152 c. 181: 14 16 15 14 16 15 15 15 16 14 15 16 SP D3 SD: 0.8429 c. M: 1.1856 c. 193: 15 17 16 15 17 16 16 16 17 15 16 17 SP D3 SD: 0.8274 c. M:-1.4935 c. 205: 16 18 17 16 18 17 17 17 18 16 17 18 SP D3 SD: 0.8938 c. M:-1.8263 c. 281: 22 24 24 22 24 24 23 23 25 22 23 25 SP SD: 0.8544 c. M: 1.5836 c. 293: 23 25 25 23 25 25 24 24 26 23 24 26 SP SD: 0.8533 c. M: 1.4383 c. 298: 23 26 25 23 26 25 25 24 27 23 24 27 SP SD: 0.9510 c. M: 1.5243 c. 305: 24 26 26 24 26 26 25 25 27 24 25 27 SP SD: 0.8871 c. M:-1.5128 c. 310: 24 27 26 24 27 26 26 25 28 24 25 28 SP SD: 0.7422 c. M: 1.1874 c. 322: 25 28 27 25 28 27 27 26 29 25 26 29 SP SD: 0.5505 c. M: 0.8756 c. 334: 26 29 28 26 29 28 28 27 30 26 27 30 SP SD: 0.3756 c. M: 0.5862 c. 346: 27 30 29 27 30 29 29 28 31 27 28 31 SP SD: 0.2220 c. M: 0.3402 c. 358: 28 31 30 28 31 30 30 29 32 28 29 32 SP SD: 0.1218 c. M: 0.2629 c. 728: 57 63 61 57 63 61 61 59 65 57 59 65 SP SD: 0.1257 c. M: 0.2261 c. 1086: 85 94 91 85 94 91 91 88 97 85 88 97 SP SD: 0.1193 c. M: 0.2382 c. 1151: 90 100 96 90 100 96 97 93 103 90 93 103 SP SD: 0.1041 c. M: 0.1876 c. 1163: 91 101 97 91 101 97 98 94 104 91 94 104 SP SD: 0.0903 c. M:-0.1848 c. 1175: 92 102 98 92 102 98 99 95 105 92 95 105 SP SD: 0.0990 c. M:-0.2102 c. 1344: 105 117 112 105 117 112 113 109 120 105 109 120 SP SD: 0.0934 c. M:-0.1849 c. 1497: 117 130 125 117 130 125 126 121 134 117 121 134 SP SD: 0.1020 c. M: 0.2175 c. 1509: 118 131 126 118 131 126 127 122 135 118 122 135 SP SD: 0.0757 c. M: 0.1587 c. 1521: 119 132 127 119 132 127 128 123 136 119 123 136 SP SD: 0.0611 c. M:-0.1144 c. 1533: 120 133 128 120 133 128 129 124 137 120 124 137 SP SD: 0.0654 c. M:-0.1344 c. 1702: 133 148 142 133 148 142 143 138 152 133 138 152 SP SD: 0.0526 c. M:-0.0907 c. 1714: 134 149 143 134 149 143 144 139 153 134 139 153 SP SD: 0.0545 c. M:-0.1039 c. 1879: 147 163 157 147 163 157 158 152 168 147 152 168 SP SD: 0.0533 c. M: 0.0941 c. 1891: 148 164 158 148 164 158 159 153 169 148 153 169 SP SD: 0.0539 c. M:-0.0874 c. 2048: 160 178 171 160 178 171 172 166 183 160 166 183 SP SD: 0.0494 c. M: 0.1031 c. 2060: 161 179 172 161 179 172 173 167 184 161 167 184 SP SD: 0.0309 c. M: 0.0566 c. 2072: 162 180 173 162 180 173 174 168 185 162 168 185 SP SD: 0.0294 c. M:-0.0538 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 2.9978 cents 2 x x x x x x 3 x x x x 4 S SD: 3.5227 cents 3 x x x x 4 x x x 5 x x 6 S SD: 5.2377 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.4302 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.8511 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.9502 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.2508 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.7649 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.8643 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.1556 cents 11 x 12:13:14:15 x 16:17:19:20:21:22 SD: 11.5088 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.5851 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.3231 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.7257 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.2386 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.5389 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 3.9298 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.8467 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.7254 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.5629 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.3965 cents 36:38:40:43:45:48:51:54:57:61:64:68:72 SD: 2.3516 cents 39:41:44:46:49:52:55:58:62:66:69:73:78 SD: 2.2043 cents 43:45:48:51:54:57:61:64:68:72:76:81:86 SD: 2.1151 cents 48:51:54:57:60:64:68:72:76:81:85:90:96 SD: 1.6287 cents 57:60:64:68:71:76:80:85:90:96:101:107:114 SD: 1.5206 cents 58:61:65:69:73:77:82:87:92:98:103:109:116 SD: 1.4598 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.4281 cents 66:70:74:78:83:88:93:99:104:111:117:124:132 SD: 1.3563 cents 73:77:82:87:92:97:103:109:115:123:130:137:146 SD: 1.3067 cents 75:79:84:89:94:100:106:112:119:126:133:141:150 SD: 0.8623 cents 91:96:102:108:114:121:128:136:144:153:161:171:182 SD: 0.7014 cents 107:113:120:127:134:142:151:160:169:180:190:201:214 SD: 0.5782 cents 160:169:179:190:201:213:226:239:253:269:284:300:319 SD: 0.5619 cents 164:173:184:195:206:218:231:245:259:276:291:308:327 SD: 0.5466 cents 166:175:186:197:208:221:234:248:262:279:295:312:331 SD: 0.4589 cents 181:191:203:215:227:241:255:271:286:304:321:340:361 SD: 0.4218 cents 182:192:204:216:228:242:257:272:288:306:323:342:363 SD: 0.3981 cents 198:209:222:235:248:264:279:296:313:333:351:372:395 SD: 0.3966 cents 214:226:240:254:268:285:302:320:338:360:380:402:427 SD: 0.3238 cents 217:229:243:258:272:289:306:324:343:365:385:407:433 SD: 0.3147 cents 257:271:288:305:322:342:362:384:406:432:456:482:513 SD: 0.2911 cents 283:299:317:336:355:377:399:423:447:476:502:531:565 SD: 0.2752 cents 288:304:323:342:361:383:406:430:455:484:511:541:575 SD: 0.2597 cents 305:322:342:362:382:406:430:456:482:513:541:572:609 SD: 0.2272 cents 324:342:363:385:406:431:457:484:512:545:575:608:647 SD: 0.1862 cents 431:455:483:512:540:574:608:644:681:725:765:809:861 SD: 0.1828 cents 449:474:503:533:563:598:633:671:710:755:797:843:896 SD: 0.1807 cents 453:478:508:538:568:603:639:677:716:762:804:850:904 SD: 0.1542 cents 465:491:521:552:583:619:656:695:735:782:825:873:928 SD: 0.1458 cents 505:533:566:600:633:672:712:755:798:849:896:948:1008 SD: 0.1239 cents 556:587:623:660:697:740:784:831:879:935:987:1044:1110 SD: 0.1148 cents